Problem: Simplify the following expression: $\sqrt{117}+\sqrt{325}-\sqrt{13}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{117}+\sqrt{325}-\sqrt{13}$ $= \sqrt{9 \cdot 13}+\sqrt{25 \cdot 13}-\sqrt{13}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{13}+\sqrt{25} \cdot \sqrt{13}-\sqrt{13}$ $= 3\sqrt{13}+5\sqrt{13}-\sqrt{13}$ Finally, simplify by combining the terms. $= ( 3 + 5 - 1 )\sqrt{13} = 7\sqrt{13}$